Calculus 1B: Integration

How long should the handle of your spoon be so that your fingers do not burn while mixing chocolate fondue? Can you find a shape that has finite volume, but infinite surface area? How does the weight of the rider change the trajectory of a zip line ride? These and many other questions can be answered by harnessing the power of the integral.

But what is an integral? You will learn to interpret it geometrically as an area under a graph, and discover its connection to the derivative. You will encounter functions that you cannot integrate without a computer and develop a big bag of tricks to attack the functions that you can integrate by hand. The integral is vital in engineering design, scientific analysis, probability and statistics. You will use integrals to find centers of mass, the stress on a beam during construction, the power exerted by a motor, and the distance traveled by a rocket.

1. Modeling the Integral

Differentials and Antiderivatives

Differential Equations

Separation of Variables

2. Theory of Integration

Mean Value Theorem

Definition of the Integral and the First Fundamental Theorem

Second Fundamental Theorem

3. Applications

Areas and Volumes

Average Value and Probability

Arc Length and Surface Area

4. Techniques of Integration

Numerical Integration

Trigonometric Powers, Trig Substitutions, Completing the Square

Partial Fractions, Integration by Parts

This course, in combination with Part 1, covers the AP* Calculus AB curriculum.

This course, in combination with Parts 1 and 3, covers the AP* Calculus BC curriculum.